Abstract: A self-adjoint operator $A\not=A_0$ is said to be a singular perturbation of the self-adjoint $A_0$ if the set $\{\psi\in D(A)\cap D(A_0)\ :\ A\psi=A_0\psi\}$ is dense. We show how to define all the singular perturbations of a given $A_0$ and then we consider the particular case in which $A_0$ is some free field Hamiltonian on Fock space.